This invention relates to navigation techniques, and more particularly relates to improved celestial navigation methods and apparatus.
In celestial navigation, it is conventional to observe the position of the stars in the sky, and to translate the observation of these fixed reference points to a determination of an actual position on the face of the earth. If one projects a line running from the center of the earth to a selected celestial body, the line intersects the surface of the earth at a point called the ground position (GP) of the celestial body. The actual location of the GP on the surface of the earth varies as the earth rotates about its axis, and further varies as the inclination of the earth changes during the rotation of the earth about the sun. The GP location is described in terms of North or South Declination, and in terms of the Greenwich Hour Angle. The Declination is simply the degrees of latitude for the GP either north or south of the 0.degree. latitude line known as the Equator. The Greenwich Hour Angle (GHA) is measured clockwise from the zero degree longitude reference line, known as the Greenwich Meridian, and is measured from zero to 360.degree.. The ground positions of numerous selected celestial bodies have been calculated and published, and are available as a function of the date and hour for each day of the year, in tabular form in a variety of almanacs such as the Nautical Alamanac published yearly by the U.S. Government Printing Office.
In conventional celestial navigation, an observer begins by observing the height of a selected celestial body above the horizon using a sextant. This reading, when corrected for the height of the observer above the surface, and also for the effects of refraction from the earth's atmosphere, becomes the observed height (Ho) of the celestial body. The exact time at which Ho was obtained is recorded as a factor in the computation.
Using the above information, a "line of position" (LOP) is then derived as hereinbelow discussed. In the conventional method, the observer first selects an assumed location: Latitude (Laa) and Longitude (Loa). Next, the GP of the selected celestial body is calculated for the exact time at which the observation of the body occurred. From these two points on the face of the earth, a calculated height (Hc) is derived for the selected celestial body. The difference in magnitude between Hc and Ho defines a distance from the assumed position to the LOP.
Given the assumed position and the GP, the bearing of the GP from the assumed position can now also be calculated. If an arc is plotted through the assumed position along this compass bearing it will connect with the GP. It is now assumed that the actual position also lies along this same line. The line of position desired is then obtained by measuring the difference between Hc and Ho either toward or away from the GP along the connecting arc as indicated by the sign of the difference and drawing the line of position perpendicular to this connecting arc at this distance from the assumed position.
The LOP so determined provides a first reference line for determining the actual position of the observer. A plurality of such lines of position are then determined by observing other celestial bodies, and the intersection of these lines of position as plotted on a suitable chart then defines a point which is the actual position of the observer. More normally, a small triangle is formed on the chart by the intersection of these lines, and the actual position is taken to be the approximate center of this triangle.
The major problem with the foregoing conventional method for obtaining an actual position from observation of celestial bodies occurs when one attempts to plot the difference between Ho and Hc on a flat plotting surface. It is well known that the transformation of a spherical surface to a planar surface for purposes of conventional plotting results in distortions in the Longitude and/or the Latitude scales. One traditional projection, the Mercator Projection, displays uniform longitudinal scales as measured along lines of latitude, but yields distorted latitude spacings as measured along lines of longitude. This distortion is ascertainable and can be corrected when plotting changes in latitude directly along a longitudinal line. If, however, a distance is plotted at an angle to the line of longitude, as is normally the case, the resulting nonlinearities introduce unascertainable errors into the conventional plot. The magnitude of this distortion increases greatly as one proceeds a further distance from the equator or as the line of direction to the GP becomes oriented in a more East West direction.
This disadvantage of the prior art is overcome by the present invention, however, and improved methods and apparatus are provided for obtaining a more accurate determination of the actual position of an observer according to celestial navigation principles.